Forward error correction (FEC) coding can reduce errors caused by noisy channels. FEC coding can be optimized by curve fitting with an extrinsic information transfer (EXIT) chart. When the channel state is time varying, the FEC coding should be changed according to the channel state. This is usually done by using adaptive coding and modulations. However, none of the existing adaptive coding methods can adjust for nonlinear channels which limits the advantage of FEC coding, especially in optical communications.
Optical communications have different characteristics than wireless communications. First, the interaction between the light signal and medium is complex. Second, optical signals are typically transmitted via a unidirectional optical fiber. Hence, optical networks use one channel from the transmitter to the receiver, and another channel from the receiver to the transmitter. Thus, the two channels are asymmetric, unlike in wireless communications, and the reverse channel does not mirror the forward channel. However, optical channels do not vary as much as wireless channels over time. Thus, channel states tend to be effective for longer time periods, and instantaneous channel state is less critical.
Adaptive precoding performs amplitude, phase control and data control to reduce errors b using a priori information of the channel state. Methods for precoding include Tomlinson-Harashima precoding, dirty paper coding, trellis shaping, time reversal precoding, inverse channel filtering, vector perturbation and predistortion. None of those methods are suited for complex time varying nonlinear channels.
Digital back-propagation (DBP) can be used for nonlinear channels in optical communications. However, DBP has many drawbacks. DBP is weak against stochastic noise, needs high-complexity operations, and a parameter mismatch to the actual channel state causes additional distortion.
In linear channels, it is known that the encoding and decoding complexity is significantly decreased, and the error probability is considerably reduced when feedback information from the receiver is available at the transmitter. An automatic-repeat request (ARQ) is one example of such. The well known Schalkwijk-Kailath (S-K) feedback coding scheme achieves channel capacity at a doubly-exponential decaying error probability without any FEC coding. However, there is no successful applications, and unified theory about the use of feedback for nonlinear channels.